The above example is not STV nor MMP so the person you are responding to is strictly correct.

The concept of proportionality is not even well-defined for STV (a problem shared by several other aspects of STV). In the example of my parent comment, where two parties are fielding candidates for 5 seats, party X receives 63% of the vote, and party Y receives 37% of the vote, STV will happily assign all 5 seats to party Y. The assignment is completely dependent on factors that weren't specified in the example.

(As a side note, Wikipedia's toy example of "STV in a party system" considers a case where three parties field candidates for 5 seats and receive 48%, 45%, and 7% of the vote, resulting in those parties respectively winning 2, 2, and 1 seats. This is about as bad in terms of proportionality as any other system [Party A has 686% of Party C's votes and 200% of the representation; Party B has merely 643% and 200% of the representation], which isn't a surprise; 5 seats don't allow for proportionality unless you're lucky enough to see a 63-37 split in the electorate. But if party-based proportionality is a concern, the correct answer is fairly obvious - the three parties should receive 2, 2, and 0 seats, with one seat going unfilled. It is interesting to me that no one ever seems to contemplate this as a possibility.)

I agree and I don't understand why some people are drawn to to STV. Among its problems is the simple fact that it is complicated. By contrast, simple approval voting (given 50 candidates, vote as much as you want and the top 5 candidates will win) will produce results just as accurate, and the math is much simpler -- every voter can easily understand what is going on.

I was drawn to STV in the past because I liked the level of control it gave voters, having them expresses preferences over parties and candidates. But now I'm more inclined to agree that its too complicated.

I don't think that the approval voting scenario you suggest is good though. If I want to elect five candidates, I want 5 candidates that represent the diversity of the population. But it seems to me that your suggested method will elect 5 candidates of the largest voting bloc, not at all what we want.

STV is pretty awesome to follow though, speaking as an elections nerd. Figuring out where the transfers will go entertains me enormously every election here in Ireland.

This is the only reason to study STV, to look at the interesting patterns. Likewise, I'm fascinated by a knowledge-graph pattern (I'm not sure if it has a name) where we use something like k-means clustering to discover less popular candidates who belong to the same cluster of voters who voted for the top candidate. I think the results would deliver good government, in that it would surface the maximum number of non-extremist ideas. But I think the math is too complicated for most people to follow, and so I think it would lack legitimacy. So I don't bother recommending it, except as a thought experiment regarding alternate systems.

As I read the above example, it leaves it undefined which proportional system is in place. As such, the statement is strictly incorrect, because it makes a general statement which isn't true of proportional systems generally.

If you read the example, you must have noticed that there is no way to interpret it as describing a system of single-transferable-vote.

The example is very explicit that votes are cast for parties and all of the benefit of receiving a vote goes to the party for which it is cast. As such, the model is only coherent if there is no such thing as voting for a candidate.

The example given mentions voting for parties, but doesn't give explicit indication how this works. Are the votes directly for parties or for candidates from those parties? It doesn't say. I suspect that you see it as explicitly talking about votes directly for parties, but I see it leaving it undefined.

But really, what exactly the original example intended to convey is a pointless pedantic argument I'm not getting into.

The crucial point is that you absolutely can have multi-member proportional districts where you vote for specific candidates. So to someone who advocated for a such multi-member districts, the contention that you have to give up voting for individual candidates simply isn't true.